Question

the equation of a line given the slope and a point
write the equation of the line that passes through the given point with the given slope.
a) $m = 4$ $p(-6,-2)$
b) $m = \frac{1}{4}$ $p(5,2)$
c) $m = \frac{-3}{2}$ $p(-4,5)$
d) $m = 3$ $p(3,-1)$

Explanation:

Step1: Use point-slope form: $y-y_1=m(x-x_1)$

For part a): $m=4$, $(x_1,y_1)=(-6,-2)$
$y-(-2)=4(x-(-6))$

Step2: Simplify to slope-intercept form

$y+2=4(x+6)$
$y+2=4x+24$
$y=4x+22$

Step1: Use point-slope form: $y-y_1=m(x-x_1)$

For part b): $m=\frac{1}{4}$, $(x_1,y_1)=(5,2)$
$y-2=\frac{1}{4}(x-5)$

Step2: Simplify to slope-intercept form

$y-2=\frac{1}{4}x-\frac{5}{4}$
$y=\frac{1}{4}x-\frac{5}{4}+\frac{8}{4}$
$y=\frac{1}{4}x+\frac{3}{4}$

Step1: Use point-slope form: $y-y_1=m(x-x_1)$

For part c): $m=-\frac{3}{2}$, $(x_1,y_1)=(-4,5)$
$y-5=-\frac{3}{2}(x-(-4))$

Step2: Simplify to slope-intercept form

$y-5=-\frac{3}{2}(x+4)$
$y-5=-\frac{3}{2}x-6$
$y=-\frac{3}{2}x-1$

Step1: Use point-slope form: $y-y_1=m(x-x_1)$

For part d): $m=3$, $(x_1,y_1)=(3,-1)$
$y-(-1)=3(x-3)$

Step2: Simplify to slope-intercept form

$y+1=3x-9$
$y=3x-10$

Answer:

a) $y=4x+22$
b) $y=\frac{1}{4}x+\frac{3}{4}$
c) $y=-\frac{3}{2}x-1$
d) $y=3x-10$